arXiv research

State spaces of multifactor approximations of nonnegative Volterra processes are linear transformations of the nonnegative orthant.

A new simulation method for Volterra processes improves convergence for rough kernels.

Study on Volterra Cox-Ingersoll-Ross process, proving asymptotic independence and ergodicity.

We consider stochastic partial differential equations appearing as Markovian lifts of matrix valued (affine) Volterra type processes from the point of view of the generalized Feller property (see e.g., \cite{doetei:10}). We introduce in particular Volterra Wishart processes with fractional kernels and values in the con…

The Volterra square-root process shows non-uniqueness of limiting distributions and regularity of its law.

Volterra square-root process boundary behavior and martingale measures

Study on fake stationary Volterra Heston model for non-stationary processes.

We simplify Volterra process predictions by reducing dimensionality and using a tailored deep learning model.

The paper introduces a method for learning nonparametric Volterra kernels using Gaussian processes.

We provide existence, uniqueness and stability results for affine stochastic Volterra equations with $L^1$-kernels and jumps. Such equations arise as scaling limits of branching processes in population genetics and self-exciting Hawkes processes in mathematical finance. The strategy we adopt for the existence part is b…

Study approximates rough stochastic volatility models using diffusion processes.

We study the regular conditional law of mixed Gaussian Volterra processes under the influence of model disturbances. More precisely, we study prediction of Gaussian Volterra processes driven by a Brownian motion in a case where the Brownian motion is not observable, but only a noisy version is observed. As an applicati…

Study on non-negative solutions for stochastic Volterra equations with jumps.

The paper derives formulas for pricing geometric Asian options in the Volterra-Heston model.

Fast simulates Volterra processes using RFF, focusing on S-fBM.

We consider so-called regular invertible Gaussian Volterra processes and derive a formula for their prediction laws. Examples of such processes include the fractional Brownian motions and the mixed fractional Brownian motions. As an application, we consider conditional-mean hedging under transaction costs in Black-Scho…

In this paper, we consider equilibrium strategies under Volterra processes and time-inconsistent preferences embracing mean-variance portfolio selection (MVP). Using a functional Itô calculus approach, we overcome the non-Markovian and non-semimartingale difficulty in Volterra processes. The equilibrium strategy is the…

Paper proves SVV model reproduces power-law skew in implied volatilities.

Defines a new short rate model and convexity adjustment formulae.

Neural SVEs model complex systems with memory, outperforming traditional methods.

This paper investigates Merton's portfolio problem in a rough stochastic environment described by Volterra Heston model. The model has a non-Markovian and non-semimartingale structure. By considering an auxiliary random process, we solve the portfolio optimization problem with the martingale optimality principle. Optim…

Study small-time CLTs for stochastic Volterra equations with various kernels.

Study proves optimal controls for stochastic Volterra equations with singular kernels.

We derive the price of a spread option based on two assets which follow a bivariate volatility modulated Volterra process dynamics. Such a price dynamics is particularly relevant in energy markets, modelling for example the spot price of power and gas. Volatility modulated Volterra processes are in general not semimart…

New financial model with sandwiched volatility for option pricing.

New method transforms complex stochastic equations into simpler ones for efficient simulation.

The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We provide closed-form expressions for the mean function and the covariance function of t…

Paper develops methods for solving complex stochastic equations using Malliavin calculus.

Researchers find the optimal exercise time for American options using a specific type of diffusion process.

This work studies nonnegativity-preserving kernels for stochastic equations and their applications.

Motivated by empirical evidence for rough volatility models, this paper investigates continuous-time mean-variance (MV) portfolio selection under the Volterra Heston model. Due to the non-Markovian and non-semimartingale nature of the model, classic stochastic optimal control frameworks are not directly applicable to t…

Paper solves Merton's portfolio problem in a non-Markovian, non-semimartingale model.

New test for point processes without strong model assumptions.

Study provides LDP for non self-similar stochastic volatility models.

New methods improve translation-equivariant neural processes for modeling unknown functions.

The paper analyzes the stationarity of stochastic Volterra integral equations and introduces fake stationary regimes.

We propose a finite difference scheme to simulate solutions to a certain type of hyperbolic stochastic partial differential equation (HSPDE). These solutions can in turn estimate so called volatility modulated Volterra (VMV) processes and Lévy semistationary (LSS) processes, which is a class of processes that have been…

We discuss the pricing and hedging of volatility options in some rough volatility models. First, we develop efficient Monte Carlo methods and asymptotic approximations for computing option prices and hedge ratios in models where log-volatility follows a Gaussian Volterra process. While providing a good fit for European…

New IBP formulae for rough stochastic Volterra processes.

The paper analyzes robustness and sensitivity of rough Volterra stochastic volatility models.

Investigates optimal investment strategies in financial markets with jumps.

We prove strong existence and uniqueness, and Hölder regularity, of a large class of stochastic Volterra equations, with singular kernels and non-Lipschitz diffusion coefficient. Extending Yamada-Watanabe's theorem, our proof relies on an approximation of the process by a sequence of semimartingales with regularised ke…

The paper studies Hawkes processes under mean-field limits and criticality conditions.

Large deviation principles for multivariate stochastic volatility models.

We study fractional stochastic volatility models in which the volatility process is a positive continuous function $σ$ of a continuous Gaussian process $\widehat{B}$. Forde and Zhang established a large deviation principle for the log-price process in such a model under the assumptions that the function $σ$ is globally…

A new method reduces Volterra kernel complexity and uncertainty quantification.

Pathwise uniqueness shown for specific stochastic equations.

Unified model for financial derivatives pricing with stochastic interest rates.